document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750248>Question 750248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5 m high vehicle needs to use the tunnel;, what is the maximum width of the vehicle that can fit through the tunnel? <BR>\n" );
document.write( "I need to draw a diagram to represent the tunnel on a coordinate number plane , and find the equation of the parabola. using algebra and coordinate geometry to determinate the maximum width of the truck<BR>\n" );
document.write( "I try to solve this problem many times but my results seems to be wrong, please help me I'm so stuck<BR>\n" );
document.write( "Ally </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456474 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Think of this as a parabola that opens downward, and<BR>\n" );
document.write( "the base, or the road, is the x-axis. The y-axis goes <BR>\n" );
document.write( "through the maximum height. The x-intercepts are at<BR>\n" );
document.write( "(  9,0 ) and ( -9,0 ), making the base 18 wide<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "The vertex of the parabola is at ( 0,10 )<BR>\n" );
document.write( "Find the equation of the parabola<BR>\n" );
document.write( "It will have the general form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-coordinate of the vertex is at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > I have stated that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+0+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+0+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+0+ ALIGN=MIDDLE  ALT=\"+b+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far, I have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+0%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+0%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Also, the vertex is at ( 0,10 ), so I can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10+=+a%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+10+=+a%2A0+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+10+ ALIGN=MIDDLE  ALT=\"+c+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and so far I have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+10+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The other points I have are ( -9,0 ) and ( 9,0 )<BR>\n" );
document.write( "If I say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0+ ALIGN=MIDDLE  ALT=\"+y+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+10+=+0+ ALIGN=MIDDLE  ALT=\"+ax%5E2+%2B+10+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-9+ ALIGN=MIDDLE  ALT=\"+x+=+-9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9+ ALIGN=MIDDLE  ALT=\"+x+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2A81+%2B+10+=+0+ ALIGN=MIDDLE  ALT=\"+a%2A81+%2B+10+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+81a+=+-10+ ALIGN=MIDDLE  ALT=\"+81a+=+-10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-10%2F81+ ALIGN=MIDDLE  ALT=\"+a+=+-10%2F81+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The whole equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-10%2F81%29%2Ax%5E2+%2B+10+ ALIGN=MIDDLE  ALT=\"+y+=+%28-10%2F81%29%2Ax%5E2+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-12%2C+12%2C+-2%2C+12%2C+%28-10%2F81%29%2Ax%5E2+%2B+10+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-12%2C+12%2C+-2%2C+12%2C+%28-10%2F81%29%2Ax%5E2+%2B+10+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "What they want to know is:<BR>\n" );
document.write( "What is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+7.5+ ALIGN=MIDDLE  ALT=\"+y+=+7.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "What is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+7.5+ ALIGN=MIDDLE  ALT=\"+y+=+7.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+ ALIGN=MIDDLE  ALT=\"+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the width of the truck.<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-10%2F81%29%2Ax%5E2+%2B+10+ ALIGN=MIDDLE  ALT=\"+y+=+%28-10%2F81%29%2Ax%5E2+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7.5+=+%28-10%2F81%29%2Ax%5E2+%2B+10+ ALIGN=MIDDLE  ALT=\"+7.5+=+%28-10%2F81%29%2Ax%5E2+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-10%2F81%29%2Ax%5E2+=+-2.5+ ALIGN=MIDDLE  ALT=\"+%28-10%2F81%29%2Ax%5E2+=+-2.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+%28+2.5%2A81%29+%2F+10+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+%28+2.5%2A81%29+%2F+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+20.25+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+20.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4.5+ ALIGN=MIDDLE  ALT=\"+x+=+4.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+=+9+ ALIGN=MIDDLE  ALT=\"+2x+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum width of the truck is 9 m<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-10%2F81%29%2Ax%5E2+%2B+10+ ALIGN=MIDDLE  ALT=\"+y+=+%28-10%2F81%29%2Ax%5E2+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-10%2F81%29%2A4.5%5E2+%2B+10+ ALIGN=MIDDLE  ALT=\"+y+=+%28-10%2F81%29%2A4.5%5E2+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-10%2F81%29%2A20.25+%2B+10+ ALIGN=MIDDLE  ALT=\"+y+=+%28-10%2F81%29%2A20.25+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-202.5%2F81+%2B+810%2F81+ ALIGN=MIDDLE  ALT=\"+y+=+-202.5%2F81+%2B+810%2F81+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+810+-+202.5+%29+%2F+81+ ALIGN=MIDDLE  ALT=\"+y+=+%28+810+-+202.5+%29+%2F+81+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+607.5%2F81+ ALIGN=MIDDLE  ALT=\"+y+=+607.5%2F81+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+7.5+ ALIGN=MIDDLE  ALT=\"+y+=+7.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );